Understanding about a dexterous robot hand's motion ranges is important to the precision grasping and precision manipulation. A planar robot hand is studied for object orientation, including ranges of motion, measures with respect to the palm, position reaching of a point in the grasped object, and rotation of the object about the reference point. The rotational dexterity index and dexterity chart are introduced and an analysis procedure is developed for calculating these quantities. A design procedure for determining the hand kinematic parameters based on a desired partial or complete dexterity chart is also developed. These procedures have been tested in detail for a planar robot hand with two 2- or 3-link fingers. The derived results are shown to be useful to performance evaluation, kinematic parameter design, and grasping motion planning for a planar robot hand.